A Treatise on the Analytic Geometry of Three Dimensions

a² b2 ax² axes axis circle circular section co-ordinates coefficients condition confocal consecutive points constant corresponding cos² cosẞ cosy cubic cz² denote determine differential direction-cosines directrix discriminant double point drawn ellipse ellipsoid envelope equal evidently focal conic foci focus geodesic given line given point Hence hyperbola hyperboloid imaginary infinity last article line joining line of curvature meets the surface normal origin osculating plane paraboloid parallel perpendicular plane at infinity plane curve plane of xy plane passing planes of circular point of contact point x'y'z polar plane principal planes quadric radii radius of curvature radius vector reciprocal represents right angles right line ruled surface second degree sphere sphero-conic square substituting surface of centres surface of revolution tangent plane tangential equation theorem triangle U₁ umbilic values vanish λ²